Schmidtnumero

Schmidtnumero, commonly called the Schmidt number (Sc), is a dimensionless quantity used in fluid mechanics and mass transfer. It expresses the ratio of momentum diffusivity to mass diffusivity of a species in a fluid and is defined as Sc = ν / D_AB = μ / (ρ D_AB), where ν is the kinematic viscosity, μ the dynamic viscosity, ρ the density, and D_AB the diffusivity of species A in B. In turbulent flows, a turbulent Schmidt number Sc_t = ν_t / D_t is also used, where ν_t and D_t are the turbulent diffusivities of momentum and species, respectively.

Interpretation and use: A high Schmidt number indicates momentum diffuses faster than mass, so mass transfer is relatively slow compared with momentum diffusion. Conversely, a small Sc means mass diffuses quickly relative to momentum. The Schmidt number is used in boundary-layer theory, similarity solutions, and correlations for mass transfer coefficients, influencing predictions in chemical engineering, environmental modeling, and microfluidics.

Typical values and relationships: In liquids, Sc often takes values from about 10^2 to 10^4 for many solutes in water, reflecting slow molecular diffusion of solutes compared with momentum diffusion. In gases such as air, Sc is usually around 0.6 to 1. For turbulent flows, Sc_t is commonly near 0.7–1.0. The Péclet number for mass transfer, Pe = UL / D_AB, can be expressed as Pe = Re · Sc, linking advection and diffusion.

Relation to other numbers: The Schmidt number is analogous to the Prandtl number (Pr = ν / α) in heat transfer, with ν as momentum diffusivity and α as thermal diffusivity.